For a digital modulation communications system, the transmitter encodes information bits into transmit symbols, usually with forward error correction coding, and further modulates the transmit symbols into waveform to travel through the physical media (or channel) of the communication link to arrive at the receiver side. The receiver samples the incoming waveform and employs various digital receiver schemes to recover the information bits from the receiving waveform under channel and noise effects.
One of the challenging tasks for implementing a robust receiver lies in the design of a symbol detector to optimally detect the transmit symbols with a maximum likelihood criterion. The design of a maximum likelihood symbol detector is particularly challenging for a MIMO communications system since it involves multi-dimensional search with an exponential growth complexity when the number of input and/or output increases. This invention discloses apparatus and methods to perform optimal maximum likelihood symbol detector that is applicable to any digitally modulated communications systems, including but not limited to MIMO communications systems.